Target Tracking

Target tracking problem• Problem statement

– A varying number of targets• Arise at random in space and time• Move with continuous motions• Persist for a random time and possibly disappear

– Positions of targets are sampled at random intervals– Measurements are noisy and

• Detection probability < 1.0• False alarms

• Goal: detect, alert, and track for each target

Frisbee model

Issues in Frisbee model

• Power savings with wake-up– Can be waked up by neighbors– Be able to form a “wakeup wavefront” that precedes

the target• Localized algorithm for defining the Frisbee

boundary– Each node autonomously decide if it is in the current

Frisbee– Adaptive fidelity

Sensing model• Sensor detection model

– Object always detected in rage R-e

– Object never detected out of range R+e

– Object possibly detected in range [R-e, R+e]

– e≈ 0.1R

ee R

Comments:• Binary detection model is most simple and reliable.• Location resolution is the sensing range for one sensor,

however, by combining multiple sensors, resolution is improved significantly.

• The sensing range don’t have to be circular.

Sensing modelWe express the general sensing model We express the general sensing model SS at at an arbitrary point an arbitrary point p p for a sensor for a sensor s s as:as:

where where d(s,p)d(s,p) is the Euclidean distance between the is the Euclidean distance between the sensor sensor ss and the point and the point pp, and positive constants , and positive constants and and K K are sensor technology dependent parametersare sensor technology dependent parameters

A Cooperative tracking algorithm• When the object enters the region where multiple

sensors can detect it, its position is within the intersection of the overlapping sensing ranges.

• Algorithm:– Each node records the duration for which the object is in

its range.– Neighboring nodes exchange these times and their

locations.– For each point of time, the object’s estimated position is

computed as the weighted average of the detecting nodes’ locations.

– A line fitting algorithm is run on the resulting set of points.

Weight assignments

Sensors that are closer to the path of the target will stay in sensor range for a longer duration.

Weight assignments• Equal weight• Proportional weight (r)

• Logarithmic weight

22 ))1((25.0

1

ftvRw

i

i

)1ln( ii tw R: sensor radiusv: estimated speedti: detection durationf: sampling frequency

Tracking methods

• One sensor at a time– Each time, only the best sensor conducts tracking

• Minimal sensor (binary) model– 1: target in range– 0: target out of range

• Hierarchical method, clusters– Acoustic sensors (delay-based collaboration)– More than 3 sensors track a target jointly

• Tree-based group collaboration

IDSQ• Information-driven sensor query• Procedures

– Each sensor performs detection by comparing measurement with a threshold (aka, likelihood ratio test)

– Detecting nodes elect a leader– The leader suppresses the other nodes to

prevent multiple tracks for the same target– The leader initializes the belief state and

reports the sensory data to the sink

IDSQDETECTION

message

IDSQ

TimestampLikelihood ratio

IDSQ

SUPPRESSION message

IDSQ

HANDOFF message

New leader reports sensory data to sink

Acoustic target trackingContext

– Delay based sound source locating algorithm, requires large number of redundant sensors for accuracy

– Tiny wireless sensors to real-world acoustic tracking applications

– Tracking only impulsive acoustic signals, such as foot steps, sniper shots, etc. No concept of tracking motion

Acoustic target tracking

• Two subsystems– Acoustic target tracking subsystem– Communication subsystem

System Overview• Acoustic target tracking subsystem

Sensor (mica motes)

Cluster Head (mono-board computer)

Sensors belong to clusters with singular cluster head.

Cluster head knows the locations of its slave sensors. Raw data gathered from sensors are processed in cluster head to generate localization results

Acoustic target tracking subsystem

• Reference-broadcast synchronization (RBS)– Physical layer broadcast

RBS

• Reference broadcasts do not have an explicit timestamp

• Receivers use reference broadcast’s arrival time as a point of reference for comparing nodes’ clocks

• Receivers synchronize with one another using the message’s timestamp (which is different from one receiver to another)

RBS illustration

A

1

3

2

4

Transmitter A broadcasts a reference packet to two receivers (e.g., 1 and 2)

Each receiver records the time that the reference was received, according to its local clock

The receivers (1 and 2) exchange their observations

Cross Correlation (to find out delays)Detect interesting sound

ClusterHead

Broadcast sound signature

Cross-correlation to detect local arrival time

SlaveSensor

Report local arrival time

Locate sound source location

Sensor (mica motes)

Cluster Head (mono-board computer)

Sensors belong to clusters with singular cluster head.

Cluster head knows the locations of its slave sensors. Raw data gathered from sensors are processed in cluster head to generate localization results

Final position fixed

Communication subsystem

• Quality-driven redundancy suppression and contention resolution (QDR)

• Overlapping of clusters’ monitoring areas (redundant areas)

• CSMA MAC

interval: time unitQ: 0 is the highest quality

Sink/Pursuer

Cluster Head

ScenarioSensor

Router

Cluster Head

Sink/Pursuer

Communication Subsystem: route back the reports generated by cluster heads

to sink

Sinkcluster covered area

router (mica motes)

cluster head

Multi-parent sink tree routing

Dynamic convoy tree-based collaboration (DCTC)

• Hierarchical (tree)• Refer to relevant slides for details

references• K. Mechitov, S. Sundresh, Y. Kwon, G. Agha, “Cooperative

Tracking with Binary-Detection Sensor Networks,” Technical Report UIUCDCS-R-2003-2379, Computer Science, UIUC, Sept. 2003

• Juan Liu, Jie Liu, James Reich, Patrick Cheung, Feng Zhao: Distributed Group Management for Track Initiation and Maintenance in Target Localization Applications. IPSN 2003: 113-128

• Qixin Wang, Wei-Peng Chen, Rong Zheng, Kihwal Lee, and Lui Sha, Acoustic Target Tracking Using Wireless Sensor Devices, Proc. of the 2nd Workshop on Information Processing in Sensor Networks (IPSN03), April 2003

• Fine-Grained Network Time Synchronization using Reference Broadcasts, Jeremy Elson, Lewis Girod and Deborah Estrin, In Proceedings of the Fifth Symposium on Operating Systems Design and Implementation (OSDI 2002)

Sensor coverage and sleeping

Assumption• Sensing effectiveness diminishes as

distance increases (monotonic)E.g.,

Homogeneous sensor nodes Non-directional sensing technology Centralized computation model

Coverage FormulationHow well can the field be

observed ?Worst Case Coverage: Maximal Breach Path Best Case Coverage: Maximal Support Path

The “paths” are generally not unique. They quantify the best and worst case observability (coverage) in the sensor field.

Maximal Breach Path (PB)Given: Field A instrumented with sensors; areas I

and F.

Problem: Identify PB, the maximal breach path in S, starting in I and ending in F.

PB is defined as a path with the property that for any point p on the path PB, the distance from p to the closest sensor is maximized.

Voronoi diagram

• The plane is partitioned by assigning every point in the plane to the nearest site

Voronoi diagram

• A Voronoi Line consists of points which are equidistant to two sites in the plane.

Enabling Step: Voronoi Diagram

By construction, each line-segment maximizes distance from the nearest point (sensor).

Consequence: Path of Maximal Breach of Surveillance in the sensor field lies on the Voronoi diagram lines.

Graph-Theoretic FormulationGiven: Voronoi diagram D with

vertex set V and line segment set L and sensors S

Construct graph G(N,E): • Each vertex viV corresponds

to a node ni N

• Each line segment li L

corresponds to an edge ei E

• Each edge eiE, Weight(ei) = Distance of li from closest sensor sk S

Formulation: Is there a path from I to F which uses no edge of weight less than K?

Finding Maximal Breach Path

Algorithm

1. Generate Voronoi Diagram2. Apply Graph-Theoretic

Abstraction3. Search for PB

Check existence of path I --> F using binary search and BFS

Delaunay triangulation• The Delaunay triangulation of a point

set is a collection of edges satisfying an "empty circle" property

• For each edge we can find a circle containing the edge's endpoints but not containing any other points

Delaunay TriangulationThe Delaunay triangulation is a triangulation which is equivalent to the nerve of the cells in a Voronoi diagram

Maximal Support PathGiven: Delaunay Triangulationof the sensor nodesConstruct graph G(N,E): The graph is dual to the Voronoi

graph previously describedFormulation: what is the path

from which the agent can best be observed while moving from I to F? (The path is embedded in the Delaunay graph of the sensors)

Solution: Similar to the max breach algorithm, use BFS and Binary Search to find the shortest path on the Delaunay graph.

I F

PS

PEAS: probing environment and adaptive sleeping

Basic Approach and assumption

• Exploit the redundancy– Keep a necessary subset of nodes working;

turn off others into sleeping– Sleeping nodes replace failed ones as

needed• Assume nodes can control the

transmitting power to reach a given radius– Variable tx power available in Berkeley

motes

Probing Environment• Each node sleeps for

a random time ts– ts follows an

exponential distribution f(ts) = e- ts

• The PROBE message is within a radius Rp (given by applications)– Rp < maximum tx

range Rt• Working nodes send

back REPLY when hearing the PROBE (also within radius Rp)

sleeping probing

working

Broadcast a PROBE within Rp(probing range)

Upon hearing a REPLY(, probing rate, is adjusted)

No REPLY is heard

Design rationale

• Adjacent working nodes keep appropriate distances (at least Rp)– Redundancy in sensing and communicating

function at appropriate levels• Probing avoid per-neighbor state about

topology information maintenance• Randomized sleeping times

– Spread over time to reduce “gap”, avoid prediction of a working node’s active time

Adaptive Sleeping• Goal: keep the aggregate PROBE rate on a

desired level _d (specified by the application)– independent from node densities at different locations,

over time• Probing rate decides how quick a dead node can

be replaced– Unnecessary overhead if too frequent – Long gaps if too slow

• Basic idea– working node measures the aggregate PROBE rate – piggybacks the info in REPLY– probing nodes adjust their rates accordingly.

How it works• A working node keeps

– Counter C– Last measurement time t0

• Increase the counter each time a PROBE is heard

• Calculate aggregate PROBE rate _a and includes it in REPLYs

• Each probing neighbor adjusts its rate accordingly

Ts Time

K wakeups

…

Measure aggregate rate: _a = K / (t - t0)

t0 t

Each probing one adjusts: _new = (_d / _a )

Example: An application wants _d = 6 times/min. Working node A has 5 sleeping neighbors, each probes at =6. Node A measures aggregate _a = 30. Each sleeping one adjusts to _new = 6(6/30)=1.2, thus new _a = 6

Maximum distance between working neighbors

• Working node A puts nodes in cell 4, 5, 6 into sleep

• To put node C in cell 2 into sleep, node B’s maximum distance to A is (1+5)Rp– Otherwise, C will be working

• When there’s at least one node in each cell, distance between working neighbors is bounded

• Theorem 3.1:when Rt > (1+5)Rp, and conditions in Blough’s Theorem 2 hold (mobicom ’02), working nodes are connected asymptotically.

A

Rp

C

BC

1

2

3

4 5

6

references• Seapahn Meguerdichian, Farinaz Koushanfar, Miodrag

Potkonjak, Mani Srivastava. "Coverage Problems in Wireless Ad-Hoc Sensor Networks." IEEE Infocom 2001, Vol. 3, pp. 1380-1387, April 2001.

• Seapahn Meguerdichian, Farinaz Koushanfar, Gang Qu, Miodrag Potkonjak. "Exposure in Wireless Ad Hoc Sensor Networks." Procs. of 7th Annual International Conference on Mobile Computing and Networking, pp. 139-150, July 2001

• Fan Ye, Gary Zhong, Jesse Cheng, Songwu Lu, Lixia Zhang, "PEAS: A Robust Energy Conserving Protocol for Long-lived Sensor Networks", in ICDCS'03, 2003